This study will be a single-arm open-label phase Ib study of neoadjuvant durvalumab +/- tremelimumab in localized / locally advanced, non-metastatic RCC patients suitable for nephrectomy. Upon selection as appropriate for study, patients will undergo computed tomography (CT)-guided biopsy of renal mass to obtain histological confirmation of diagnosis, and immunologic characterization of the RCC tumor. Peripheral blood will also be drawn at time of screening. Patients will subsequently receive systemic neoadjuvant treatment in one of 5 cohorts as defined below. Following systemic therapy, patients will undergo nephrectomy. Type of surgery (open vs. minimally invasive, radical vs. partial) and template for lymph node dissection are at the discretion of surgeon. Timing of surgery in relation to adverse events and/or treatment for adverse events from neoadjuvant dosing of study drugs is at the discretion of the surgeon. Adjuvant therapy will be administered within 4-6 weeks of surgery. Subsequent follow-up will then be completed to assess adverse event resolution and long-term outcomes.